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|Title:||On the grading numbers of direct products of chains|
|Authors:||Chen, C.C. |
|Source:||Chen, C.C.,Koh, K.M.,Lee, S.C. (1984-03). On the grading numbers of direct products of chains. Discrete Mathematics 49 (1) : 21-26. ScholarBank@NUS Repository.|
|Abstract:||For a finite lattice L, denote by l*(L) and l*(L) respectively the upper length and lower length of L. The grading number g(L) of L is defined as g(L) = l*(Sub(L))-l*(Sub(L)) where Sub(L) is the sublattice-lattice of L. We show that if K is a proper homomorphic image of a distributive lattice L, then l*(Sub(K)) < l*(Sub(L)); and derive from this result, formulae for l*(Sub(L)) and g(L) where L is a product of chains. © 1984.|
|Source Title:||Discrete Mathematics|
|Appears in Collections:||Staff Publications|
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